Train and Tunnel Paradox

Here's a favorite relativity paradox. This appears in the book as
Review Question 7.13.

Suppose that a train robber decides to
stop a train inside tunnel. The proper length of the train is 60 m,
while the proper length of the tunnel is 50 m. The train is traveling
at 4/5 the speed of light. According to proper lengths, the train
would not fit inside the tunnel. But the robber plans to use
relativity to his advantage. The length of the moving train in the
rest frame of the tunnel, and of the robber, is 36 m. The robber
computes this and decides to trap the train inside the tunnel, since,
in his frame, the train should fit. From the point of view of the
train's engineer, however, the tunnel is only 30 m long, just
half the length of the train. The engineer knows that his 60 m train
will not fit completely into the tunnel. The robber thinks that the
train will fit, whereas the engineer is sure it will not. But either
the train will fit, or it will not; it cannot do both. Who is
correct?

Hints:

Consider the following events: the locomotive
enters the tunnel. The locomotive reaches the end of the tunnel. The
caboose enters the tunnel. The caboose reaches the end of the tunnel.
Which events are necessarily causally connected? Which are not? Draw
a spacetime diagram and label these four events. In which order do
these four events occur in the robber's frame? In the train's frame?

A version of this paradox often found in books on relativity is one
where a pole-vaulter runs with a pole into a barn. The pole's rest length
is greater than the rest length of the barn. Does the pole fit?